We present a spectrophotometric analysis of S Ori J053825.4-024241, a candidate member close to the substellar boundary of the young (1-8 Myr), nearby (~360 pc) σ Orionis star cluster. Our optical and near-infrared photometry and low-resolution spectroscopy indicate that S Ori J053825.4-024241 is a likely cluster member with a mass estimated from evolutionary models at 0.06+0.07-0.02 M_&sun;, which makes the object a probable brown dwarf. The radial velocity of S Ori J053825.4-024241 is similar to the cluster systemic velocity. This target, which we have classified as an M 6.0±1.0 low-gravity object, shows excess emission in the near-infrared and anomalously strong photometric variability for its type (from the blue to the J band), suggesting the presence of a surrounding disc. The optical spectroscopic observations show a continuum excess at short wavelengths and a persistent and resolved Hα emission (pseudo-equivalent width of ~-250 Å) in addition to the presence of other forbidden and permitted emission lines, which we interpret as indicating accretion from the disc and possibly mass loss. We conclude that despite the low mass of S Ori J053825.4-024241, this object exhibits some of the properties typical of active classical T Tauri stars.